1- Given the family of curves y=1/(x+C).
Find the family of orthogonal trajectories.

For this problem, I took the first derivative of y---> y'=-1/(x+C)^2. from here, I cannot find the value of C since (x+C)^2=-1/y' which is impossible.
What can I do here?

Given the family of curves

,

rearrange to give:

and differentiate:

or:

.

So now we know that the slope of any curve of the family that passes
through is . So the slope of a curve orthogonal to a member
of the family passing through is . So a curve in the orthoganal family
satisfies the ODE: